Monodromy of Hyperelliptic Abelian Integrals
Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)
We want to show that in the case of Hamiltonians of the form
where f(x) is a polynomial of degree n, the existence of a tangential center implies that either P dx — Qdy is relatively exact, or the polynomial f(x) is composite. That is, it can be expressed as a polynomial of a polynomial, f(x) = a(b(x)), in a non-trivial way.
$$ H(x,y) = y^2 + f(x), $$
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© Birkhäuser Verlag 2007